Abstract

In active scalar polarimetric imaging systems, the illumination and analysis polarization states are degrees of freedom that can be used to maximize the performance. These optimal states depend on the statistics of the noise that perturbs image acquisition. We investigate the problem of optimization of discrimination ability (contrast) of such imagers in the presence of three different types of noise statistics frequently encountered in optical images (Gaussian, Poisson, and Gamma). To compare these different situations within a common theoretical framework, we use the Bhattacharyya distance and the Fisher ratio as measures of contrast. We show that the optimal states depend on a trade-off between the target/background intensity difference and the average intensity in the acquired image, and that this trade-off depends on the noise statistics. On a few examples, we show that the gain in contrast obtained by implementing the states adapted to the noise statistics actually present in the image can be significant.

(a) Variation of θopt as a function of ε in the scenario of Subsection 3.A, for diattenuation d=1, in the presence of Gaussian, Poisson, and Gamma noise sources. (b) Azimuth of the optimal states for the three types of noises, ε=20°, and d=1.

Evolution of the contrast with parameter ε in the presence of (a) Gaussian noise, (b) Poisson noise, and (c) Gamma noise, in the scenario of Subsection 3.A, for d=1. Figure (c) has been obtained with S and T partially polarized (‖s‖=‖t‖=0.99) in order to have contrasts that are not infinite.

Images in the presence of (a)–(c) Gaussian, (d)–(f) Poisson, and (h)–(j) Gamma noise of a target characterized by a Mueller matrix Mb and a background characterized by a Mueller matrix Ma (ρ=0.14), for the scenario of Subsection 3.B. In each case, the image is obtained with optimal states computed with the hypothesis of the presence of Gaussian, Poisson, and Gamma noise (respectively from left to right). The number of photons by pixel is I0=100 and the standard deviation of the Gaussian noise is equal to 10. The Gamma noise is of order L=1.